I had an identical problem when the Apple store replaced my ipad mini this week. Symptoms were: Apple replaced my ipad, I kept the SIM card and LTE data seemed to work, but I could not access my cellular account details.
It took three trips to the verizon store, and several tech support calls, but it's finally working!
1) check your monthly verizon ipad plan payment email, find the "phone number" for your ipad, and go to a verizon mobilestore
2) get a new SIM card from the verizon support technitians, put it in your ipad (data won't work, but you should see 3G signal, not LTE)
3) Verizon support at the store will try (and fail repeatedly) to get this SIM card onto your account. (Their system doesn't allow this to work correctly for the prepaid data plans)
4) call verizon mobile tech support from the store with the store support people, give them the new SIM cards number, and your iPads IMEI -- they will connect both with your data account, and probably reset your accounts password
5) restart your device, wait for signal and reprovision your device again (this time it will work, and the signal will disappear/go to "searching"), wait for signal again, and restart your ipad again. You should see LTE again, and data/internet should work again.
6) go to settings > view account, and log into your account, with the reset password they email you
7) it will now ask you to update your password (do it)
8) you should see your account details again
9) check that data/internet/email works still... Restart your ipad and confirm, etc
10) rejoice, because holy crap it worked
Be persistent, and be patient. May the force be with you all!